| The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is |
A) 5
B) 25
C) 100
D) 125
Correct Answer: B
Solution :
| Let LCM be x and HCF be y. |
| According to the question, |
| \[LCM=4\times HCF\]\[\Rightarrow \]\[x=4y\] |
| and \[LCM+HCF=125\] |
| \[x+y=125\] |
| On putting the value of x, we get |
| \[5y=125\]\[\Rightarrow \]\[y=25\] |
| \[\therefore \] \[HCF=25\] |
| and \[LCM=4\times 25=100\] |
| We know that, |
| HCF \[\times \] LCM = First number \[\times \] Second number |
| \[\therefore \] Second number |
| \[=\frac{\text{HCF}\times \text{LCM}}{\text{First}\,\text{number}}=\frac{100\times 25}{100}=25\] |
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